Hello Sanjid, thank you for your question.
Here is an example of a system that uses a PbA battery model autoElectrical
I recommend you use Simscape to create an equivalent circuit that captures all the electrochemical effects that you need and at the same time gives you adequate fidelity.
Stateflow is a great tool to model state transitions such as the ones you mention above.
Regarding parameters, I would at least consider OCV, internal resistance, dynamic resistance, self-discharge, and the Peukert effect, and all of these should depend on temperature using lookup tables.
Please let me know if this helps.
Best regards,
Javier
